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  <title>Simple 3D Flexible Spacecraft</title>
                                  
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<div align="center">     <img src="Simple3DFlexSC.GIF" alt="Title"
 width="544" height="64">
     
<div align="left"><b><u>Simulation Control</u></b><br>
   <b>time step</b>:         Time step for the numerical integration routine<br>
   <b>time</b>:                Duration of the simulation periond in seconds<br>
   <br>
    <b><u>Description</u></b><br>
   A flexible spacecraft is modeled as a central rigid body with two massless 
 beams<br>
   attachd symmetrically to the side of the central body. Each beam has a 
<br>
   concentrated mass at the tip. The flexibility comes from the flexural
rigidity  EI of <br>
   the beams. Although the flexible elements are constrained to move in 1-2 
 plane<br>
   only, the applet is able to simulate the effect of flexibility on the
spacecraft  <br>
   attitude in three dimensional space.<br>
    <img src="Flexible202D.GIF"
 alt="2D Flexible Spacecraft Illustration" width="540" height="424">
    <br>
    <b><u>Inputs</u></b><br>
   <b>Ixx, Iyy, Izz</b>:        &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Principal moments if inertia<br>
   <b>m</b>:                    &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160; Tip mass (kg)<br>
   <b>a</b>:                     &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Distance as
indicated in the illustration (m)<br>
   <b>L</b>:                     &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Length of the 
beam as illustrated (m)<br>
   <b>EI</b>:                    &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Flexural rigidity 
(N m2)<br>
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   <b><u>Initial Condition</u></b><br>
   <b>u1</b>:                    &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Position of the
first mass<br>
   <b>u2</b>:                    &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Position of the
second mass<br>
   <b>psi, theta, phi</b>:      &#160;&#160;&#160; &#160;&#160;&#160; Euler angles in a sequence of 3-2-1<br>
   <b>u1Dot</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Velocity of the first 
mass<br>
   <b>u2Dot</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Velocity of the second 
mass<br>
   <b>psiDot</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Time rate of psi angle<br>
   <b>thetaDot</b> :           &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Time rate of theta angle<br>
   <b>phiDot</b>:               &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Time rate of phi angle<br>
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